1.3 Scott’s Macho March Recall: Linear Quadratic Exponential A Solidify Understanding Task Recall: Linear Quadratic Exponential How can you distinguish between them? Recursive Model or Equation Explicit Model or Equation

1.3 Scott’s Macho March A Solidify Understanding Task After looking in the mirror and feeling flabby, Scott decided that he really needs to get in shape. He joined a gym and added push-ups to his daily exercise routine. He started keeping track of the number of push-ups he completed each day in the bar graph below, with day one showing he completed three push-ups. After four days, Scott was certain he can continue this pattern of increasing the number of push-ups for at least a few months. 1 2 3 4 1. Model the number of push-ups Scott will complete on any given day. Include both explicit and recursive equations. Create a table of Days and Pushups.

M(x) Total Pushups, Recursive Model M(x) Total Pushups, Explicit Model Scott’s gym is sponsoring a “Macho March” promotion. The goal of “Macho March” is to raise money for charity by doing push-ups. Scott has decided to participate and has sponsors that will donate money to the charity if he can do a total of at least 500 push-ups, and they will donate an additional $10 for every 100 push-ups he can do beyond that. 2. Estimate the total number of push-ups that Scott will do in a month if he continues to increase the number of push-ups he does each day in the pattern shown above. 3. How many pushups will Scott have done after a week? 4. Model the total number of pushups that Scott has done on any given day during “Macho March”. Include both recursive and explicit equations. Use a table to organize the data. 5. Will Scott meet his goal and earn the donation for the charity? Will he get a bonus? If so, how much? Explain. x Days f(x) Pushups that day M(x) Total Pushups, Recursive Model M(x) Total Pushups, Explicit Model First Difference Second Difference 1 2 3 4 5 x

Computational Skills 1. Multiplying binomials page 15

13. x F(x_ -3 24 -2 22 -1 20 18 1 16 2 14 3 12 14. x F(x) -3 48 -2 22 -1 6 1 4 2 18 3 42 15. x F(x) -3 4 -2 1 2 9 3 16 Pattern: Recursive equation: Pattern: Recursive equation: Pattern: Recursive equation:

16. Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Draw figure 5. Predict the number of squares in figure 30. Show what you did to get your prediction. Organize the data into a table to find a recursive and explicit model for the figure pattern above.

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